$g(t)=(t+1)^2-20.25$ 1) What are the zeros of the function? Write the smaller $t$ first, and the larger $t$ second. $\text{smaller }t=$
Answer: $\begin{aligned} (t+1)^2-20.25&=0 \\\\ (t+1)^2&=20.25 \\\\ \sqrt{(t+1)^2}&=\sqrt{20.25} \\\\ t+1&=\pm 4.5 \\\\ t&=\pm4.5-1 \\\\ t={-5.5}&\text{ or }t={3.5} \end{aligned}$ $g(t)$ is given in vertex form: $g(t)=(t-({-1}))^2{-20.25}$ So the vertex of the parabola is at $({-1},{-20.25})$. In conclusion, $\begin{aligned} \text{smaller }t&=-5.5 \\\\ \text{larger }t&=3.5 \end{aligned}$ The vertex of the parabola is at $(-1,-20.25)$